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Show that (x^5-5x^4+5x^3-1) has a local ...

Show that `(x^5-5x^4+5x^3-1)` has a local maximum when x = 1, a local minimum when x = 3, and neither x = 0

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PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. The function f(x)=oversetxunderset(-1)intt(e^t-1)(t-1)(t-2)^3(t-3)^5 d...

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  2. Use the function f(x)=x^(1//x),xgt0 to determine the bigger of the two...

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  3. Show that (x^5-5x^4+5x^3-1) has a local maximum when x = 1, a local mi...

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  4. Find the point on the parabola y^2=2x which is closest to the point (1...

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  5. In a right -angled triangle, prove that r+2R=S.

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  6. Show that the semivertical angle of a cone of maximum volume and of gi...

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  7. Let f(x)={(|x-2|+a^2-9a-9,ifxlt2, 2x-3 ,ifxge2:} Then find value of 'a...

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  8. Find the values of 'm' for which the equation x^4-(m-3)x^2+m=0 has Fo...

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  9. The difference between the greatest and least values of the function f...

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  10. The tangent and normal to the curve y=2sinx+sin2x are drown at P(x=pi/...

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  11. Show that the sum of the intercepts of the tangent to the curve sqrtx+...

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  12. Find the point on the curve y-e^(xy)+x=0. At which we have vertical ta...

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  13. Find the lengths of tangent, subtangent, normal and subnormal to y^2=4...

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  14. If the length of subnormal is equal to length of subtangent at a point...

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  15. Find the angle of intersection between the following curves, y^2=4x an...

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  16. Show that x=y^2 and xy = k cut orthogonally if 8k^2=1

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  17. Show that curves ax^2+by^2=1 and cx^2+dy^2=1 intersect orthogonally if...

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  18. Prove that the curve (x/a)^n+(y/b)^n=2 touches the straught line x/a+y...

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  19. Prove that all points of the curve y^2=4a[x+asinx/a] at which the lang...

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  20. Verify Rolle's theorem for f(x)=x^3(x-1)^2 in the interval 0lexle1

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